%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PUZ061+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:58:17 PM UTC 2025 % Result : Theorem 3.69s 3.85s % Output : Proof 3.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : PUZ061+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 20:49:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.69/3.85 SZS status Theorem for theBenchmark.p % 3.69/3.85 SZS output start Proof for theBenchmark.p % 3.69/3.85 Clause #0 (by assumption #[]): Eq % 3.69/3.85 (Not % 3.69/3.85 (∀ (Peanuts John Bill Sue Apples Chicken : Iota), % 3.69/3.85 And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.85 (∀ (X : Iota), food X → likes John X)) % 3.69/3.85 (food Apples)) % 3.69/3.85 (food Chicken)) % 3.69/3.85 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.85 (eats Bill Peanuts)) % 3.69/3.85 (alive Bill)) % 3.69/3.85 (∀ (X : Iota), eats Bill X → eats Sue X)) % 3.69/3.85 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.85 likes John Peanuts)) % 3.69/3.85 True % 3.69/3.85 Clause #1 (by clausification #[0]): Eq % 3.69/3.85 (∀ (Peanuts John Bill Sue Apples Chicken : Iota), % 3.69/3.85 And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.85 (∀ (X : Iota), food X → likes John X)) % 3.69/3.85 (food Apples)) % 3.69/3.85 (food Chicken)) % 3.69/3.85 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.85 (eats Bill Peanuts)) % 3.69/3.85 (alive Bill)) % 3.69/3.85 (∀ (X : Iota), eats Bill X → eats Sue X)) % 3.69/3.85 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.85 likes John Peanuts) % 3.69/3.85 False % 3.69/3.85 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.69/3.85 Eq % 3.69/3.85 (Not % 3.69/3.85 (∀ (John Bill Sue Apples Chicken : Iota), % 3.69/3.85 And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.85 (∀ (X : Iota), food X → likes John X)) % 3.69/3.85 (food Apples)) % 3.69/3.85 (food Chicken)) % 3.69/3.85 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.85 (eats Bill (skS.0 0 a))) % 3.69/3.85 (alive Bill)) % 3.69/3.85 (∀ (X : Iota), eats Bill X → eats Sue X)) % 3.69/3.85 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.85 likes John (skS.0 0 a))) % 3.69/3.85 True % 3.69/3.85 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.69/3.85 Eq % 3.69/3.85 (∀ (John Bill Sue Apples Chicken : Iota), % 3.69/3.85 And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.85 (∀ (X : Iota), food X → likes John X)) % 3.69/3.85 (food Apples)) % 3.69/3.85 (food Chicken)) % 3.69/3.85 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.85 (eats Bill (skS.0 0 a))) % 3.69/3.85 (alive Bill)) % 3.69/3.85 (∀ (X : Iota), eats Bill X → eats Sue X)) % 3.69/3.85 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.85 likes John (skS.0 0 a)) % 3.69/3.85 False % 3.69/3.85 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.69/3.85 Eq % 3.69/3.85 (Not % 3.69/3.85 (∀ (Bill Sue Apples Chicken : Iota), % 3.69/3.85 And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And % 3.69/3.85 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.85 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.85 (food Apples)) % 3.69/3.85 (food Chicken)) % 3.69/3.85 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.85 (eats Bill (skS.0 0 a))) % 3.69/3.85 (alive Bill)) % 3.69/3.85 (∀ (X : Iota), eats Bill X → eats Sue X)) % 3.69/3.85 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.87 likes (skS.0 1 a a_1) (skS.0 0 a))) % 3.69/3.87 True % 3.69/3.87 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.69/3.87 Eq % 3.69/3.87 (∀ (Bill Sue Apples Chicken : Iota), % 3.69/3.87 And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.87 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.87 (food Apples)) % 3.69/3.87 (food Chicken)) % 3.69/3.87 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.87 (eats Bill (skS.0 0 a))) % 3.69/3.87 (alive Bill)) % 3.69/3.87 (∀ (X : Iota), eats Bill X → eats Sue X)) % 3.69/3.87 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.87 likes (skS.0 1 a a_1) (skS.0 0 a)) % 3.69/3.87 False % 3.69/3.87 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.69/3.87 Eq % 3.69/3.87 (Not % 3.69/3.87 (∀ (Sue Apples Chicken : Iota), % 3.69/3.87 And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.87 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.87 (food Apples)) % 3.69/3.87 (food Chicken)) % 3.69/3.87 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.87 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.87 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.87 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats Sue X)) % 3.69/3.87 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.87 likes (skS.0 1 a a_1) (skS.0 0 a))) % 3.69/3.87 True % 3.69/3.87 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 3.69/3.87 Eq % 3.69/3.87 (∀ (Sue Apples Chicken : Iota), % 3.69/3.87 And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.87 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.87 (food Apples)) % 3.69/3.87 (food Chicken)) % 3.69/3.87 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.87 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.87 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.87 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats Sue X)) % 3.69/3.87 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.87 likes (skS.0 1 a a_1) (skS.0 0 a)) % 3.69/3.87 False % 3.69/3.87 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.87 Eq % 3.69/3.87 (Not % 3.69/3.87 (∀ (Apples Chicken : Iota), % 3.69/3.87 And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.87 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.87 (food Apples)) % 3.69/3.87 (food Chicken)) % 3.69/3.87 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.87 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.87 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.87 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.87 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.87 likes (skS.0 1 a a_1) (skS.0 0 a))) % 3.69/3.87 True % 3.69/3.87 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.87 Eq % 3.69/3.87 (∀ (Apples Chicken : Iota), % 3.69/3.87 And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And % 3.69/3.87 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.87 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.87 (food Apples)) % 3.69/3.89 (food Chicken)) % 3.69/3.89 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.89 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.89 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.89 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.89 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.89 likes (skS.0 1 a a_1) (skS.0 0 a)) % 3.69/3.89 False % 3.69/3.89 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (Not % 3.69/3.89 (∀ (Chicken : Iota), % 3.69/3.89 And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.89 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.89 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.89 (food Chicken)) % 3.69/3.89 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.89 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.89 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.89 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.89 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.89 likes (skS.0 1 a a_1) (skS.0 0 a))) % 3.69/3.89 True % 3.69/3.89 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (∀ (Chicken : Iota), % 3.69/3.89 And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And (∀ (X Y : Iota), And (alive Y) (eats Y Chicken) → likes Y X) % 3.69/3.89 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.89 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.89 (food Chicken)) % 3.69/3.89 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.89 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.89 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.89 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.89 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.89 likes (skS.0 1 a a_1) (skS.0 0 a)) % 3.69/3.89 False % 3.69/3.89 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (Not % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.69/3.89 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.89 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.89 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.69/3.89 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.89 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.89 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.89 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.89 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.89 likes (skS.0 1 a a_1) (skS.0 0 a))) % 3.69/3.89 True % 3.69/3.89 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And % 3.69/3.89 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.69/3.89 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.89 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.89 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.69/3.89 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.89 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.89 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.89 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.91 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) → % 3.69/3.91 likes (skS.0 1 a a_1) (skS.0 0 a)) % 3.69/3.91 False % 3.69/3.91 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.69/3.91 Eq % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.69/3.91 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.91 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.91 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.69/3.91 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.91 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.91 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.91 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.91 (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X)) % 3.69/3.91 True % 3.69/3.91 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (likes (skS.0 1 a a_1) (skS.0 0 a)) False % 3.69/3.91 Clause #16 (by clausification #[14]): Eq (∀ (Y : Iota), alive Y → ∀ (X : Iota), not_killed_by Y X) True % 3.69/3.91 Clause #17 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.69/3.91 Eq % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And % 3.69/3.91 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.69/3.91 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.91 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.91 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.69/3.91 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.91 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.91 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.91 (∀ (X : Iota), eats (skS.0 2 a a_1 a_2) X → eats (skS.0 3 a a_1 a_2 a_3) X)) % 3.69/3.91 True % 3.69/3.91 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (alive a → ∀ (X : Iota), not_killed_by a X) True % 3.69/3.91 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (alive a) False) (Eq (∀ (X : Iota), not_killed_by a X) True) % 3.69/3.92 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (alive a) False) (Eq (not_killed_by a a_1) True) % 3.69/3.92 Clause #22 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.69/3.92 Eq % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.69/3.92 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.92 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.92 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.69/3.92 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.92 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.92 (alive (skS.0 2 a a_1 a_2))) % 3.69/3.92 True % 3.69/3.92 Clause #25 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (alive (skS.0 2 a a_1 a_2)) True % 3.69/3.92 Clause #26 (by clausification #[22]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.69/3.92 Eq % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.69/3.92 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.69/3.92 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.69/3.92 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.69/3.92 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.69/3.92 (eats (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 3.69/3.92 True % 3.69/3.92 Clause #27 (by superposition #[25, 20]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (not_killed_by (skS.0 2 a a_1 a_2) a_3) True) % 3.69/3.92 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota), Eq (not_killed_by (skS.0 2 a a_1 a_2) a_3) True % 3.69/3.92 Clause #29 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (eats (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 3.69/3.92 Clause #30 (by clausification #[26]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.69/3.92 Eq % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And % 3.69/3.92 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.78/3.93 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.78/3.93 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.78/3.93 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.78/3.93 (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X)) % 3.78/3.93 True % 3.78/3.93 Clause #33 (by clausification #[30]): Eq (∀ (X : Iota), (Exists fun Y => And (eats Y X) (not_killed_by Y X)) → food X) True % 3.78/3.93 Clause #34 (by clausification #[30]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.78/3.93 Eq % 3.78/3.93 (And % 3.78/3.93 (And % 3.78/3.93 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.78/3.93 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.78/3.93 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.78/3.93 (food (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.78/3.93 True % 3.78/3.93 Clause #35 (by clausification #[33]): ∀ (a : Iota), Eq ((Exists fun Y => And (eats Y a) (not_killed_by Y a)) → food a) True % 3.78/3.93 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (Exists fun Y => And (eats Y a) (not_killed_by Y a)) False) (Eq (food a) True) % 3.78/3.93 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (food a) True) (Eq (And (eats a_1 a) (not_killed_by a_1 a)) False) % 3.78/3.93 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (food a) True) (Or (Eq (eats a_1 a) False) (Eq (not_killed_by a_1 a) False)) % 3.78/3.93 Clause #39 (by superposition #[38, 29]): ∀ (a a_1 a_2 : Iota), % 3.78/3.93 Or (Eq (food (skS.0 0 a)) True) (Or (Eq (not_killed_by (skS.0 2 a a_1 a_2) (skS.0 0 a)) False) (Eq False True)) % 3.78/3.93 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Eq (food (skS.0 0 a)) True) (Eq (not_killed_by (skS.0 2 a a_1 a_2) (skS.0 0 a)) False) % 3.78/3.93 Clause #42 (by superposition #[41, 28]): ∀ (a : Iota), Or (Eq (food (skS.0 0 a)) True) (Eq False True) % 3.78/3.93 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (food (skS.0 0 a)) True % 3.78/3.93 Clause #46 (by clausification #[34]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.78/3.93 Eq % 3.78/3.93 (And % 3.78/3.93 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.78/3.93 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.78/3.93 (food (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.78/3.93 True % 3.78/3.93 Clause #50 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.78/3.93 Eq % 3.78/3.93 (And (∀ (X Y : Iota), And (alive Y) (eats Y (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → likes Y X) % 3.78/3.93 (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X)) % 3.78/3.93 True % 3.78/3.93 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (∀ (X : Iota), food X → likes (skS.0 1 a a_1) X) True % 3.78/3.93 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Eq (food a → likes (skS.0 1 a_1 a_2) a) True % 3.78/3.93 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Eq (food a) False) (Eq (likes (skS.0 1 a_1 a_2) a) True) % 3.78/3.93 Clause #55 (by superposition #[54, 43]): ∀ (a a_1 a_2 : Iota), Or (Eq (likes (skS.0 1 a a_1) (skS.0 0 a_2)) True) (Eq False True) % 3.78/3.93 Clause #63 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Eq (likes (skS.0 1 a a_1) (skS.0 0 a_2)) True % 3.78/3.93 Clause #64 (by superposition #[63, 15]): Eq True False % 3.78/3.93 Clause #66 (by clausification #[64]): False % 3.78/3.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------